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The preliminary estimates of the empirical path term account for the intrinsic and scattering attenuation, geometrical spreading, and the general increase of duration with distance due to wave propagation and scattering at each hypocentral distance for each frequency.
The predicted waveforms are much more similar to the observed waveforms at FKIH05, in both the time and frequency domains, than the observed waveforms at FKI006 even without correcting for differences in the path term.
If the epicentral distance is large compared with the interstation distance, we can neglect the small difference in the source terms at each station and attribute the differences in amplitude to the relative site amplification factor and differences in the path term.
Our prediction method assumes that the difference in seismic intensity between two stations is mainly caused by the difference in site amplification; however, numerical shake prediction method is based on the physics of wave propagation, so that effects of path term are included in their method.
To obtain an empirical estimate of the path term in Eq. (1), a coda normalization technique (Aki, 1980; Frankel et al., 1990) can be used to eliminate the source and site terms by taking the ratio of the peak amplitude carried by S or Lg waves in filtered time histories to the root-mean-square (rms) amplitude of the stable seismic coda.
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Because of dense seismic networks and highly active seismicity in Japan, we were able to estimate site amplification factor with simple assumptions in source and path terms.
At interstation distances larger than the value of 10 km we used, the source and path terms would surely have a greater influence on intensity predictions.
The other issue is the Doppler shift of the direct-path term in the estimated CSI.
In addition, the spectral shift of the direct-path term could only rotate g 0,q in (6) through a certain angle and therefore could not change the MT location information in ϕ 0,m,q,1≤m≤M q.
Therefore, the effective CFR for the m-th antenna is obtained by first computing the left-hand side of (15), then translating the frequency of the remaining shortest-path term to zero, and finally averaging the result over the frequency domain, i.e., G_{m,q}=sum_{k=-K}^{K}G_{k,m,q}/ 2K+1), (16).
Localization is achieved using the direct-path terms on the basis of the maximum likelihood principle.
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